\documentclass{article}
\newtheorem{axiom}{Axiom}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
\newcommand\unicdcdcdbg{\cup}
\newcommand\unicdcdbdgd{\setminus}
\newcommand\unicdcdcdjd{\cap}
\newcommand\unicdcdadad{\forall}
\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
\newcommand\uniddcgcg{\lambda}
\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t43\_quaterni (TMGuyhSzyGWaS5qbNZyCGGpeVHVWHsdRnjE)}
\maketitle
Let $ v1\_quaterni : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k31\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_quaterni : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k17\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_real\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k18\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k19\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k20\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k28\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k30\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_quaterni : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k26\_quaterni : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_quaterni : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k12\_quaterni : {\iota}$ be given.
Let $ k5\_quaterni : {\iota}$ be given.
Let $ k11\_quaterni : {\iota}$ be given.
Let $ k4\_quaterni : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k23\_quaterni : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k25\_quaterni : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xcmplx\_0 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}((k17\_quaterni~(k28\_quaterni~X0)=\\
k1\_real\_1~(k17\_quaterni~X0)){\unicdcdcdhd}((k18\_quaterni~(k28\_quaterni~X0)=\\
k1\_real\_1~(k18\_quaterni~X0)){\unicdcdcdhd}((k19\_quaterni~(k28\_quaterni~X0)=\\
k1\_real\_1~(k19\_quaterni~X0)){\unicdcdcdhd}(k20\_quaterni~(k28\_quaterni~X0)=\\
k1\_real\_1~(k20\_quaterni~X0)))))\end{array}
\label{hyp:ehedbdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_quaterni}~{X0}})}{\unicdbdjdcd}{({{{k31\_quaterni}~{X0}}={{k30\_quaterni}~{X0}}})}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgddbdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_quaterni}~{X0}})}{\unicdbdjdcd}{({{{k28\_quaterni}~{X0}}={{k8\_quaterni}~{X0}}})}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdidpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_quaterni~X0){\unicdcdcdhd}(v1\_quaterni~X1)){\unicdbdjdcd}(\\
k26\_quaterni~X0~X1=k7\_quaterni~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdgdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
{{k12\_quaterni}={k5\_quaterni}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdcdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
{{k11\_quaterni}={k4\_quaterni}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdbdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~k1\_numbers){\unicdbdjdcd}(k6\_quaterni~X0~X1~X2~X3=k7\_quaterni~\\
(k7\_quaterni~(k23\_quaterni~X0~(k25\_quaterni~X1~k1\_xcmplx\_0))~\\
(k25\_quaterni~X2~k11\_quaterni))~(k25\_quaterni~X3~k12\_quaterni)))))\end{array}
\label{hyp:mghdgdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_quaterni~X0){\unicdcdcdhd}(v1\_quaterni~X1)){\unicdbdjdcd}(\\
v1\_quaterni~(k7\_quaterni~X0~X1))\end{array}
\label{hyp:ggdggdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_quaterni}~{k5\_quaterni}}\label{hyp:ggdgfdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_quaterni}~{k4\_quaterni}}\label{hyp:ggdgedpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_quaterni}~{k1\_xcmplx\_0}}\label{hyp:ggdgddpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k1\_numbers){\unicdcdcdhd}(v1\_quaterni~\\
X1)){\unicdbdjdcd}(v1\_quaterni~(k25\_quaterni~X0~X1))\end{array}
\label{hyp:ggdgbdddpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k1\_numbers){\unicdcdcdhd}(v1\_quaterni~\\
X1)){\unicdbdjdcd}(v1\_quaterni~(k23\_quaterni~X0~X1))\end{array}
\label{hyp:ggdgbdcdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_quaterni}~{X0}})}{\unicdbdjdcd}{({{v1\_quaterni}~{({{k8\_quaterni}~{X0}})}})}}}\label{hyp:egehpflgidpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}(m1\_subset\_1~(k20\_quaterni~X0)~k1\_numbers)\end{array}
\label{hyp:egehpflgcdadpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}(m1\_subset\_1~(k19\_quaterni~X0)~k1\_numbers)\end{array}
\label{hyp:egehpflgbdjdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}(m1\_subset\_1~(k18\_quaterni~X0)~k1\_numbers)\end{array}
\label{hyp:egehpflgbdidpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}(m1\_subset\_1~(k17\_quaterni~X0)~k1\_numbers)\end{array}
\label{hyp:egehpflgbdhdpfbhfhbgehfgchogjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}(k30\_quaterni~X0=k26\_quaterni~(\\
k26\_quaterni~(k23\_quaterni~(k17\_quaterni~X0)~(k25\_quaterni~(\\
k1\_real\_1~(k18\_quaterni~X0))~k1\_xcmplx\_0))~(k25\_quaterni~(k1\_real\_1~\\
(k19\_quaterni~X0))~k11\_quaterni))~(k25\_quaterni~(k1\_real\_1~(\\
k20\_quaterni~X0))~k12\_quaterni))\end{array}
\label{hyp:egcdcdpfbhfhbgehfgchogjg}
\end{equation}
\begin{theorem}\label{thm:ehedddpfbhfhbgehfgchogjg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_quaterni~X0){\unicdbdjdcd}(k31\_quaterni~X0=k6\_quaterni~(k17\_quaterni~\\
X0)~(k1\_real\_1~(k18\_quaterni~X0))~(k1\_real\_1~(k19\_quaterni~X0))~\\
(k1\_real\_1~(k20\_quaterni~X0)))\end{array}$$
\end{theorem}
\end{document}
